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essentials of statistics
The Basic Practice Of Statistics 5th Edition David S Moore - Solutions
If there is no difference in emissions between the attacked group and the control group, the mean of W in the previous exercise is(a) 39. (b) 78. (c) 6.2.25.37 Suppose that the 12 observations in Exercise 25.35 were Control group 14.4 15.2 12.6 11.9 5.1 8.0 Attacked group 12.6 15.3 25.2 19.8 17.1
When some plants are attacked by leaf-eating insects, they release chemical compounds that repel the insects. Here are data on emissions of one compound by plants attacked by leaf bugs and by plants in an undamaged control group:Control group 14.4 15.2 12.6 11.9 5.1 8.0 Attacked group 10.6 15.3
You interview 75 students in their freshman year and again in their senior year. Each interview includes a test of knowledge of world affairs. To assess whether there has been a significant change from freshman to senior year, you use the(a) Wilcoxon rank sum test.(b) Wilcoxon signed rank test.(c)
You interview college students who have done community service and another group of students who have not. To compare the scores of the two groups on a test of attitude toward people of other races, you use the(a) Wilcoxon rank sum test.(b) Wilcoxon signed rank test.(c) Kruskal-Wallis test.
A study of “road rage” gives randomly selected drivers a test that measures “angry/threatening driving.”You wonder if the scores go down with age. You compare the scores for three age groups: less than 30 years, 30 to 55 years, and over 55 years. You use the(a) Wilcoxon rank sum test.(b)
Which test? Example 24.4 describes one of the experiments done by Kathleen Vohs and her coworkers to demonstrate that even being reminded of money makes people more self-sufficient and less involved with other people. Here are three more of these experiments. For each experiment, which statistical
Conditions for ANOVA. Examine the data for the year 2004. The conditions for ANOVA inference are not met. In what way do these data fail to meet the conditions?(It is not very surprising that in 5 ANOVAs one will fail to satisfy our quite conservative conditions.)
The results for 2001. Your work in Exercise 24.30 shows that there were signifi-cant differences in mean plant biomass among the three treatments in 2003. Do a complete analysis of the data for 2001 and report your conclusions.
Plot the means. Starting from the data in Table 24.6, you can calculate the mean plant biomass for each treatment in each year as follows:Year 2001 2002 2003 2004 2005 Winter 132.58 203.33 205.17 223.58 332.84 Spring 257.69 388.85 315.39 299.54 289.66 Control 81.67 180.31 136.65 201.07 257.37 Plot
analyzed the effect of logging on number of trees. Exercise 24.8 concludes that it would be risky to use ANOVA to analyze richness. Use software to analyze the effect of logging on the number of species.(a) Make a table of the group means and standard deviations. Do the standard deviations satisfy
Logging in the rain forest: species counts. Table 24.2 gives data on the number of trees per forest plot, the number of species per plot, and species richness. Exercise
Durable press fabrics wrinkle less. The data in Exercise 24.35 show that durable press treatment greatly reduces the breaking strength of cotton fabric. Of course, durable press treatment also reduces wrinkling. How much? “Wrinkle recovery angle”measures how well a fabric recovers from
Durable press fabrics are weaker. “Durable press” cotton fabrics are treated to improve their recovery from wrinkles after washing. Unfortunately, the treatment also reduces the strength of the fabric. A study compared the breaking strength of untreated fabric with that of fabrics treated by
Does polyester decay? How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried polyester strips in the soil for different lengths of time, then dug up the strips and measured the force required to break them. Breaking strength is easy to measure and is a good
Does nature heal best? Our bodies have a natural electrical field that helps wounds heal. Might higher or lower levels speed healing? An experiment with newts investigated this question. Newts were randomly assigned to five groups.In four of the groups, an electrode applied to one hind limb (chosen
Which blue is most blue? The color of a fabric depends on the dye used and also on how the dye is applied. This matters to clothing manufacturers, who want the color of the fabric to be just right. Dye fabric made of ramie with the same “procion blue” die applied in four different ways. Then
Can you hear these words? Figure 24.11 displays the Minitab output for oneway ANOVA applied to the hearing data described in Exercise 24.29. The response variable is “Percent,”and “List” identifies the four lists of words. Based on this analysis, is there good reason to think that the four
More rain for California? The changing climate will probably bring more rain to California, but we don’t know whether the additional rain will come during the winter wet season or extend into the long dry season in spring and summer. Kenwyn Suttle of the University of California at Berkeley and
Can you hear these words? To test whether a hearing aid is right for a patient, audiologists play a tape on which words are pronounced at low volume. The patient tries to repeat the words. There are several different lists of words that are supposed to be equally difficult. Are the lists equally
Plants defend themselves. When some plants are attacked by leaf-eating insects, they release chemical compounds that attract other insects that prey on the leafeaters.A study carried out on plants growing naturally in the Utah desert demonstrated both the release of the compounds and that they not
A medical study. The Qu´ebec (Canada) Cardiovascular Study recruited men aged 34 to 64 at random from towns in the Qu´ebec City metropolitan area. Of these, 1824 met the criteria (no diabetes, free of heart disease, and so on) for a study of the relationship between being overweight and medical
Test accommodations. Many states require schoolchildren to take regular statewide tests to assess their progress. Children with learning disabilities who read poorly may not do well on mathematics tests because they can’t read the problems.Most states allow “accommodations” for
Writing essays. Do strategies such as preparing a written outline help students write better essays? College students were divided at random into four groups of 20 students each, then asked to write an essay on an assigned topic. Group A (the control group) received no additional instruction. Group
Morning or evening? Are you a morning person, an evening person, or neither?Does this personality trait affect how well you perform? A sample of 100 students took a psychological test that found 16 morning people, 30 evening people, and 54 who were neither. All the students then took a test of
The P-value 0.014 in the output may not be accurate because the conditions for ANOVA are not satisfied. The most serious violation of the conditions is that(a) the sample standard deviations are too different.(b) there is an extreme outlier in the data.(c) the data can’t be regarded as random
The conclusion of the ANOVA test is that(a) there is quite strong evidence (P = 0.014) that the mean CFUs are not the same in all four seasons.(b) there is quite strong evidence (P = 0.014) that the mean CFUs are much lower in winter than in any other season.(c) the data give no evidence (P =
In all, we would have to give 6 two-sample confidence intervals to compare all pairs of seasons. The weakness of doing this is that(a) we don’t know how confident we can be that all 6 intervals cover the true differences in means.(b) 90% confidence is OK for one comparison, but it isn’t high
We might use the two-sample t procedures to compare summer and winter. The conservative 90% confidence interval for the difference in the two population means is(a) 1929.5 ± 458.3. (b) 1929.5 ± 1078.4. (c) 1929.5 ± 1458.4.
The most striking conclusion from the numerical summaries for the turkey processing plant is that(a) there appears to be little difference among the seasons.(b) on the average, CFUs are much lower in winter than in other seasons.(c) the air in the plant is clearly unhealthy.
The F distributions are(a) a family of distributions with bell-shaped density curves centered at 0.(b) a family of distributions that are right-skewed and take only values greater than 0.(c) a family of distributions that are left-skewed and take values between 0 and 1.The air in poultry processing
The alternative hypothesis for the ANOVA F test in the previous exercise is(a) the mean hours of sleep in the groups are all the same.(b) the mean hours of sleep in the groups are all different.(c) the mean hours of sleep in the groups are not all the same.
A study of the effects of smoking classifies subjects as nonsmokers, moderate smokers, or heavy smokers. The investigators interview a sample of 200 people in each group. Among the questions is “How many hours do you sleep on a typical night?”The degrees of freedom for the ANOVA F statistic
The purpose of analysis of variance is to compare(a) the variances of several populations.(b) the proportions of successes in several populations.(c) the means of several populations.
Confidence intervals for the intercept (optional). The output in Figure 23.7 allows you to calculate confidence intervals for both the slope β and the intercept αof the population regression line of BAC on beers in the population of all students.Confidence intervals for the intercept α have the
Tests for the intercept (optional). Figure 23.7 (page 611) gives Minitab output for the regression of blood alcohol content (BAC) on number of beers consumed.The t test for the hypothesis that the population regression line has slope β = 0 has P < 0.001. The data show a positive linear
Standardized residuals (optional). Software often calculates standardized standardized residuals residuals as well as the actual residuals from regression. Because the standardized residuals have the standard z-score scale, it is easier to judge whether any are extreme.Figure 23.13 and the data
A lurking variable (optional). Return to the data on selling price versus appraised value for beachfront condominiums that are the basis for the Check Your Skills Exercises 23.16 to 23.24. Prices for beachfront property were rising rapidly during this period. Because property is reassessed just
was that organic matter settling down from the top layers of the ocean is the main source of DNA on the seafloor. An important piece of evidence is the relationship between DNA and phytopigments. Do the data in the file ex23-39.dat give good reason to think that phytopigment concentration helps
DNA on the ocean floor. Another conclusion of the study introduced in Exercise
Sulfur, the ocean, and the sun. Sulfur in the atmosphere affects climate by in-fluencing formation of clouds. The main natural source of sulfur is dimethylsulfide(DMS) produced by small organisms in the upper layers of the oceans. DMS production is in turn influenced by the amount of energy the
Beavers and beetles. Exercise 5.51 (page 157) describes a study that found that the number of stumps from trees felled by beavers predicts the abundance of beetle larvae. Is there good evidence that more beetle larvae clusters are present when beavers have left more tree stumps? Estimate how many
A big toe problem. Table 7.4 (page 194) and Exercises 7.42 and 7.44 describe the relationship between two deformities of the feet in young patients. Metatarsus abductus (MA) may help predict the severity of hallux abducto valgus (HAV).The paper that reports this study says, “Linear regression
Squirrels and their food supply. Exercise 7.25 (page 188) gives data on the abun-dance of the pine cones that red squirrels feed on and the mean number of offspring per female squirrel over 16 years. The strength of the relationship is remarkable because females produce young before the food is
Time at the table: prediction. Rachel is another child at the nursery school of Exercise 23.38. Over several months, Rachel averages 40 minutes at the lunch table.Give a 95% interval to predict Rachel’s average calorie consumption at lunch.Exercises 23.41 to 23.45 ask practical questions of
DNA on the ocean floor. We think of DNA as the stuff that stores the genetic code. It turns out that DNA occurs, mainly outside living cells, on the ocean floor.It is important in nourishing seafloor life. Scientists think that this DNA comes from organic matter that settles to the bottom from the
Time at the table. Does how long young children remain at the lunch table help predict how much they eat? Here are data on 20 toddlers observed over several months at a nursery school.9 “Time”is the average number of minutes a child spent at the table when lunch was served. “Calories” is
Our brains don’t like losses. Exercise 4.29 (page 116) describes an experiment that showed a linear relationship between how sensitive people are to monetary losses (“behavioral loss aversion”) and activity in one part of their brains (“neural loss aversion”).(a) Make a scatterplot with
Sparrowhawk colonies: residuals. The regression of number of new birds that join a sparrowhawk colony on the percent of adult birds in the colony that return from the previous year is an example of data that satisfy the conditions for regression inference well. Here are the residuals for the 13
Predicting tropical storms: residuals. Make a stemplot of the residuals (round to the nearest tenth) from your regression in Exercise 23.33. Explain why your plot suggests that we should not use these data to get a prediction interval for the number of storms in a single year.
Sparrowhawk colonies. One of nature’s patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Exercise 4.28 (page 116) gives data for 13 colonies of sparrowhawks.In Exercises 4.28 and 5.36 (page 153), you
Predicting tropical storms. Exercise 5.53 (page 158) gives data on William Gray’s predictions of the number of named tropical storms in Atlantic hurricane seasons from 1984 to 2007. Use these data for regression inference as follows.(a) Does Professor Gray do better than random guessing? That is,
Fidgeting keeps you slim: inference. Our first example of regression (Example 5.1, page 126) presented data showing that people who increased their nonexercise activity (NEA) when they were deliberately overfed gained less fat than other people. Use software to add formal inference to the data
Manatees: estimation. The output in Figure 23.14 includes prediction of manatees killed when there are 1,050,000 boats registered in Florida. Give 95% intervals for(a) the increase in manatees killed for each additional 1000 boats registered.(b) the number of manatees that will be killed next year
Manatees: do more boats bring more kills? The output in Figure 23.14 omits the t statistics and their P-values. Based on the information in the output, is there good evidence that the number of manatees killed increases as the number of boats registered increases? State hypotheses and give a test
Manatees: conditions for inference. We know that there is a strong linear relationship.Let’s check the other conditions for inference. Figure 23.14 includes a table of the two variables, the predicted values ˆy for each x in the data, the residuals,and related quantities. (This table is stored
shows part of the Minitab regression output. Exercises 23.29 to 23.31 analyze the manatee data.
Casting aluminum: residuals. The output in Figure 23.13 includes a table of the the x and y variables, the fitted values ˆy for each x, the residuals, and some related quantities. (This table is stored as ex23-28.dat on the text CD and Web site.)(a) Plot the residuals against thickness (the
Casting aluminum: intervals. The output in Figure 23.13 includes prediction for piston wall thickness x∗ = 0.5 inch. Use the output to give 90% intervals for(a) the slope of the population regression line of gate velocity on piston thickness.(b) the average gate velocity for a type of piston with
Casting aluminum: is there a relationship? Figure 23.13 leaves out the t statistics and their P-values. Based on the information in the output, test the hypothesis that there is no straight-line relationship between thickness and gate velocity. State hypotheses, give a test statistic and its
Too much nitrogen? Burning fossil fuels deposits extra nitrogen on the land. Too much nitrogen can reduce the variety of plants by favoring rapid growth of some species—think of putting fertilizer on your lawn to help grass choke out weeds. A study of 68 grassland sites in Britain measured
Hamada owns a unit in this building appraised at $802,600. The Minitab output includes prediction for this appraised value. She can be 95% confident that her unit would sell for between(a) $920,900 and $1,013,700.(b) $810,700 and $1,123,900.(c) $945,700 and $988,900.
A 95% confidence interval for the population slope β is(a) 1.0466 ± 0.2415. (b) 1.0466 ± 149.5706. (c) 1.0466 ± 0.2387.
Confidence intervals and tests for these data use the t distribution with degrees of freedom(a) 14. (b) 15. (c) 16.
The regression standard error for these data is(a) 0.1126. (b) 69.7299. (c) 79.49.
Minitab shows that the P-value for this test is(a) 0.132. (b) less than 0.001. (c) 0.861.
Is there significant evidence that selling price increases as appraised value increases?To answer this question, test the hypotheses(a) H0: β = 0 versus Ha: β > 0.(b) H0: β = 0 versus Ha: β = 0.(c) H0: α = 0 versus Ha: α > 0.
The slope β of the population regression line describes(a) the exact increase in the selling price of an individual unit when its appraised value increases by $1000.(b) the average increase in selling price in a population of units when appraised value increases by $1000.(c) the average selling
What is the correlation between selling price and appraised value?(a) 0.1126 (b) 0.861 (c) 0.928
The equation of the least-squares regression line for predicting selling price from appraised value is(a) price = 79.49 + 0.1126 × appraised value.(b) price = 127.27 + 1.0466 × appraised value.(c) price = 1.0466 + 127.27 × appraised value.
Party support in full. Use the full table to analyze the differences in political party support among levels of education. The sample is so large that the differences are bound to be highly significant, but give the chi-square statistic and its P-value nonetheless. The main challenge is in seeing
Party support in brief. Make a 2 × 5 table by combining the counts in the three rows that mention Democrat and in the three rows that mention Republican and ignoring strict independents and supporters of other parties.We might think of this table as comparing all adults who lean Democrat and all
Other parties. Give a 95% confidence interval for the proportion of adults who support “other parties.”
Market research. Before bringing a new product to market, firms carry out exten-sive studies to learn how consumers react to the product and how best to advertise its advantages. Here are data from a study of a new laundry detergent.23 The subjects are people who don’t currently use the
The Mediterranean diet. Cancer of the colon and rectum is less common in the Mediterranean region than in other Western countries. The Mediterranean diet contains little animal fat and lots of olive oil. Italian researchers compared 1953 patients with colon or rectal cancer with a control group of
How are schools doing? The nonprofit group Public Agenda conducted tele-phone interviews with a stratified sample of parents of high school children. There were 202 black parents, 202 Hispanic parents, and 201 white parents. One question asked was “Are the high schools in your state doing an
Students and catalog shopping. What is the most important reason that stu-dents buy from catalogs? The answer may differ for different groups of students. Here are results for samples of American and East Asian students at a large midwestern university:20 American Asian Save time 29 10 Easy 28 11
Smoking among French men. In the United States, there is a strong relationship between education and smoking: well-educated people are less likely to smoke.Does a similar relationship hold in France? Here is a two-way table of the level of education and smoking status (nonsmoker, former smoker,
Animal testing. “It is right to use animals for medical testing if it might save human lives.” The General Social Survey asked 1152 adults to react to this statement. Here is the two-way table of their responses:Male Female Strongly agree 76 59 Agree 270 247 Neither agree nor disagree 87 139
Sorry, no chi-square. Does eating chocolate trigger headaches? To find out, women with chronic headaches followed the same diet except for eating chocolate bars and carob bars that looked and tasted the same. Each subject ate both chocolate and carob bars in random order with at least three days
Sorry, no chi-square. Here is more information about Internet use by students at Penn State, based on a random sample of 1852 undergraduates. Explain why it is not correct to use a chi-square test on this table to compare the University Park and commonwealth campuses.University Park Commonwealth
Sorry, no chi-square. How do U.S. residents who travel overseas for leisure differ from those who travel for business? The following is the breakdown by occupation.17 Leisure travelers Business travelers Professional/technical 36% 39%Manager/executive 23% 48%Retired 14% 3%Student 7% 3%Other 20%
Sorry, no chi-square. We would prefer to learn from teachers who know their subject. Perhaps even preschool children are affected by how knowledgeable they think teachers are. Assign 48 3- and 4-year-olds at random to be taught the name of a new toy by either an adult who claims to know about the
Sexy magazine ads? Look at full-page ads in magazines with a young adult read-S TE Pership. Classify ads that show a model as “not sexual”or “sexual”depending on how the model is dressed (or not dressed). Here are data on 1509 ads in magazines aimed at young men, at young women, or at young
I think I’ll be rich by age 30. A sample survey asked young adults (aged 19 to 25), S TE P“What do you think are the chances you will have much more than a middle-class income at age 30?” The Minitab output in Figure 22.8 shows the two-way table and related information, omitting a few
Unhappy rats and tumors. Some people think that the attitude of cancer patients can influence the progress of their disease. We can’t experiment with humans, but here is a rat experiment on this theme. Inject 60 rats with tumor cells and then divide them at random into two groups of 30. All the
Opinions about the death penalty. The data for comparing two sample proportions can be presented in a two-way table containing the counts of successes and failures in both samples, with two rows and two columns. Here is an example from the General Social Survey. The question was “Do you favor or
Did the randomization work? After randomly assigning subjects to treatments in a randomized comparative experiment, we can compare the treatment groups to see how well the randomization worked.We hope to find no significant differences among the groups. A study of how to provide premature infants
Do you use cocaine? Sample surveys on sensitive issues can give different results depending on how the question is asked. A University of Wisconsin study divided 2400 respondents into 3 groups at random. All were asked if they had ever used cocaine. One group of 800 was interviewed by phone; 21%
Free speech for racists? The General Social Survey (GSS) asked this question:“Consider a person who believes that Blacks are genetically inferior. If such a person wanted to make a speech in your community claiming that Blacks are inferior, should he be allowed to speak, or not?”Here are the
Got broadband? A sample survey by the Pew Internet and American Life Project asked a random sample of adults about use of the Internet. One question was whether the subject had a broadband Internet connection at home. Here is a twoway table of home broadband use by type of community:10 Community
The most important fact that allows us to trust the results of the chi-square test is that(a) the sample is large, 4877 teenagers in all.(b) the sample is close to an SRS of all teenagers.(c) all of the cell counts are greater than 100.
Software gives chi-square statistic χ2 = 69.8 for this table. From the table of critical values, we can say that the P-value is(a) between 0.0025 and 0.001.(b) between 0.001 and 0.0005.(c) less than 0.0005.
The alternative hypothesis for the chi-square test for this two-way table is(a) Female and male teenagers do not have the same distribution of opinions about marriage.(b) Female teenagers are more likely than male teenagers to think it is almost certain they will be married in ten years.(c) Female
The null hypothesis for the chi-square test for this two-way table is(a) Equal proportions of female and male teenagers are almost certain they will be married in ten years.(b) There is no difference between female and male teenagers in their distributions of opinions about marriage.(c) There are
The degrees of freedom for the chi-square test for this two-way table are(a) 4. (b) 8. (c) 20.
The term in the chi-square statistic for the cell of females who respond “almost certain” is about(a) 17.6. (b) 15.6. (c) 0.1.
The expected count of females who respond “almost certain” is about(a) 464.6. (b) 891.2. (c) 1038.8.
The percent of the females in the sample who responded “almost certain” is(a) higher than the percent of males who felt this way.(b) about the same as the percent of males who felt this way.(c) lower than the percent of males who felt this way.
The percent of the females in the sample who responded “almost certain” is about(a) 44.7%. (b) 39.6%. (c) 33.6%.
The number of female teenagers in the sample is(a) 4877. (b) 2625. (c) 2252.
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